The basic function of a communication system is to send information over a communication channel from a source that generates the information to one or more destinations. In a digital communication system, the information is converted into a digital format and then transmitted over the communication channel. The transmission of digital information is subject to the adverse effects of the communication channel, such as co-channel and adjacent channel interference, noise, dispersion, and fading. These effects introduce errors into the transmitted data stream. These effects are particularly severe in a radio communication system.
In 1948, Claude E. Shannon demonstrated in a landmark paper that proper encoding of the digital information prior to transmission may reduce the errors introduced by a noisy channel to any desired level. Encoding is the process of adding redundancy to information prior to its transmission so that errors which may occur during transmission can be detected and/or corrected. At the receiving end, the decoder makes use of the redundant information and a priori knowledge of the coding scheme to detect and/or correct errors that may have occurred during transmission.
Many types of error correction codes have been devised, including block codes and convolutional codes. Turbo codes, which were introduced in 1993, are considered to have high error correction capability and good performance and have been selected for use in third and fourth generation mobile communication systems. In its most basic form, a turbo code comprises two parallel systematic convolutional encoders connected in parallel by an interleaver. The first encoder operates on the original input bits and generates first parity bits. The interleaver permutes the order of the input bits and the interleaved bits are supplied to the second encoder. The second encoder operates on the interleaved bits output by the interleaver and generates second parity bits. For each input bit, three output bits are generated: the input bit and two parity bits.
Iterative decoding is used at the receiver to decode turbo codes. A basic turbo decoder comprises two soft-input, soft-output (SISO) decoders connected in series by an interleaver. The received bits are input to the first decoder. The first decoder uses the received bits and extrinsic information fed back from the second decoder to generate a soft estimate of the original input bits expressed as a log-likelihood ratio and extrinsic information that is supplied to the second decoder. The extrinsic information output from the first decoder is interleaved before it is input to the second decoder to compensate for the interleaving performed at the encoder. The second decoder generates a more refined log-likelihood estimate of the original input bit and extrinsic information that is fed back to the first decoder. A final decision about the bit is made by hard limiting the soft estimate output by the second decoder.
The properties of the interleaver are important to the performance of a turbo coder. When turbo codes were first introduced, pseudorandom interleavers were proposed. For long block lengths, pseudorandom interleavers are problematic because the interleavers require large storage resources. At small block lengths, pseudorandom interleavers do not perform well. Other types of interleavers have been proposed including inter-block permutation (IBP) interleavers and almost regular permutation (ARP) interleavers. More recently, quadratic permutation polynomial (QPP) interleavers have been proposed. QPP interleavers provide good performance, have low computational complexity, and allow contention free parallel decoding. However, the design of good QPP interleavers is difficult because the number of potential QPP coefficients is too large to simulate and test individually. Some general guidelines for selecting QPP parameters have been proposed, but do not always yield the best results.